Model order reduction based on Runge–Kutta neural networks

Abstract Model order reduction (MOR) methods enable the generation of real-time-capable digital twins, with potential to unlock various novel value streams in industry. While traditional projection-based are robust and accurate for linear problems, incorporating machine learning deal nonlinearity becomes a new choice reducing complex problems. These kinds independent numerical solver full model keep nonintrusiveness whole workflow. Such usually consist two steps. The first step is dimension by method, second reconstruction neural network (NN). In this work, we apply some modifications both steps respectively investigate how they impacted testing three different simulation models. all cases Proper orthogonal decomposition used reduction. For step, effects generating snapshot database constant input parameters compared time-dependent parameters. types NN architectures compared: multilayer perceptron (MLP), explicit Euler (EENN), Runge–Kutta (RKNN). MLPs learn system state directly, whereas EENNs RKNNs derivative predict as integrator. tests, show their advantage architecture informed higher-order strategy.